I'm afraid it's vanishingly unlikely, unless the game itself has a usename+login for an associated website and saves the game there.
One tiny possibility: If there was a manual or iCloud backup of the phone taken shortly before the twatty child deleted it, then that could be restored. Manual would be using iTunes on a pc/mac; iCloud would be automatic last night when it was plugged in and connected to wifi.
If it has been plugged in to charge this evening, it's probably too late - there's only the most recent backup.
If it hasn't yet, make sure there's a backup available (look in iTunes, or for iCloud then on the phone Settings > iCloud > Storage > Manage Storage, and then select your device, tap iCloud backup and check the "last successful backup" date.) ONLY IF THERE IS A GOOD BACKUP, reset the phone then re-download the backup:
Go to Settings > General > Reset on your iPhone, then choose the 'Erase All Content And Settings' option.
After that finishes and reboots you will be on the setup screensWhen it offers, don't set up as new phone but 'Restore from iCloud Backup', then log into the iCloud account.
Continue to 'Choose backup,' then choose the iCloud backup you need to view.
Wait for the device to finish download the iCloud backup. Once it is complete, you can access